Existing glass bubbles have wide utility for many purposes, but they have only limited utility when very high crushing strengths are needed. For example, existing glass bubbles have only limited utility as a filler for polymeric parts made by injection molding operations, which subject the bubbles to high pressure.
Theoretically, the collapse strength of an individual glass bubble should be as given by a formula devised by M. A. Krenzke and R. M. Charles ("Elastic Buckling Strength of Spherical Glass Shells," David Taylor Model Basin Report No. 1759, September, 1963), ##EQU1## where "E" is Young's modulus for the glass of the bubbles, "h" is the thickness of the wall of the bubbles, "r" is the radius of the bubble, and "V" is Poisson's ratio for the glass.
In actual practice, when a batch of glass bubbles is tested, a vast majority of bubbles in the batch collapse at a pressure substantially less than the theoretical strength, e.g., because of inherent flaws in the structure of the bubbles. One practical measure of strength for a batch of glass bubbles is to determine the pressure required (in the test described in ASTM D-3102-72, with glycerol used in place of water) to obtain a ten-volume-percent collapse of bubbles. By this test, commercial glass bubbles of the highest known strength (made under the teachings of U.S. Pat. No. 3,365,315) exhibit a ten-volume-percent collapse at a pressure of about 4300 psi (29.6 N/m.sup.2), which is less than 30 percent of the theoretical strength for those bubbles.